The Z expansion technique for calculating atomic properties has been extended to the calculation of dipole hyperpolarizabilities. The leading two terms are of order Z−10 and Z−11 in the closed-shell case and of order Z−7 and Z−8 in the open-shell case. The corresponding coefficients have been calculated exactly, and also within the uncoupled Hartree-Fock approximation. Numerical results have been obtained for the ground states of the helium, lithium, and beryllium isoelectronic sequences, and for the metastable S1 and S3 states of the helium sequence. Our Hartree-Fock values for the ground states of the helium sequence are in good agreement with those of Langhoff, Lyons, and Hurst. However, the value derived from the leading two terms of the exact Z expansion for neutral helium is about 40% lower, and even for N5+, the discrepancy is still 10%. For the other sequences, the discrepancies are much larger, extending even to the signs of the hyperpolarizabilities of the lithium and beryllium sequences. The polarizabilities of the above sequences are also included for comparison with other data to indicate the rate of convergence of the asymptotic Z expansions.